Bellatrix escaped never making it to the cell at Azkaban with her name on it. Bellatrix manages to find her way into Hogwarts to get rid of the one person that could destroy her Dark Lord, Harry Potter. Partly insane she reasoned that if he never got his letter then he would turn into an Obscurial. As she was looking for his name McGonagall comes into the room. Bellatrix fled before Minerva could realize what happened, leaving a mess behind of all the future students' names on the ground. It just so happened that Hermione's letter never got to her from all the mix-up.